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It’s easier to accept John Nash than the goddess Namagiri

Saturday, January 7th, 2017

[ by Charles Cameron — delighted to find Ramanujan is not alone in dreaming of mathematics ]

When the Hinduism Today writer above says people found Ramanujan‘s assertion that his equations were given him in dreams by the local goddess Namagiri “irksome” he was understing the case: many mathematicians are allergic to the idea of a goddess providing inspiration to a mathematician in a devotional dream state. Thus Krishnaswami Alladi, in his Review of the Movie on the mathematical genius Ramanujan, writes:

The legend is that the Hindu Goddess Namagiri came in Ramanujan’s dreams and gave him these formulae..

See? It’s a legend, a priori, since “goddesses” don’t exist.

John Nash, he of the Beautiful Mind, game theory equilibria, and the Nobel Prize, on the other hand — if he provides inspiration to a fellow mathematician in a dream?

Why, his solution can be acknowledged as such in a learned paper..

Coffee & Donuts, a topological DoubleQuote

Monday, October 10th, 2016

[ by Charles Cameron — sadly, now dunkin’ diabetes ]

Some might claim that Dunkin is the link between Coffee and Donuts — it’s certainly a link I’ve appreciated myself on more than one occasion. Here’s another, and arguably more subtle linkage — topology.

In verbal format, it’s a mathematician’s inside joke:

The joke goes about topologists is that they can’t tell the difference between a coffee mug and a doughnut. For those who are not familiar with topology, topology is the study of geometrical objects where you don’t care about lengths and you don’t care about angles, what matters is how the spatial relations relate to each other.

Even better, here’s the same joke, illustrated — or refuted, if you prefer — in video by a master maker:

The only problem here — it’ll all prove a little pointless if you dunk your donut into the coffee cup without first supplying some coffee..

But morphing! What an ingenious way to provide and prove a DoubleQuote!

On the felicities of graph-based game-board design: nine

Sunday, October 9th, 2016

[ by Charles Cameron — if the territory is graphical, so’s the map ]

Terrain, with its named places and transportation links between them, is graphical, as illustrated in this map:

It makes me wonder how often graph theory (of the sort that gives us the Königsberg Bridge Problem, see the first post in this series) is applied to troop movements — as it often is to public transportation (see the upcoming tenth post).


My next example of the use of a node-and-edge graphical design both puzzles and intrigues me:

It puzzles me, because I can’t quitec grasp what Raza Rumi — a very bright fellow — is up to in choosing this particular illustration. And it intrigues me, because once on a vision quest I glimpsed an outstretched eagle’s or hawk’s wing, with a similar graphical overlay of its structural essence. It’s a sight I’ve never forgotten, an exquisite linking of the real and abstract worlds, and one that I’m sadly ill-equipped to reproduce visually myself. Words don’t do it justice.


My third example, as you can see, is taken from a learned paper describing the use of graphs to illustrate musical compositions according to a strictly defined protocol:

What interests me here — aside from the fact that any of these digrams could be used as a board in a sufficiently complex HipBone or Sembl game — is that I ran across this particular paper within 24 hours of reading m’friend Bill Benzon‘s account of his friend Michael Bérubé and his son Jamie, introduced in this tweet:

Bill’s post Jamie’s Investigations, Part 1: Emergence to which his tweet refers us — is illustrated thus:


Michael Bérubé, we read, has recently published a book about Jamie, who has Down’s, Life as Jamie Knows It: An Exceptional Child Grows Up, and it contains a series of Jamie’s drawings, of which this is one example.

Bill, who is himself the author of Beethoven’s Anvil: Music in Mind and Culture, notes “Jamie loves music, and his dad is a rock-and-roll drummer, so’s his older brother Nick, I believe.” And here’s the clincher — he then asks:

In what way are these drawings like drum beats?

So that’s two examples of novel visual representations of musical pattern in just two days, earlier this week.


Enough for now — onwards to On the felicities of graph-based game-board design: ten — a long, fascinating post IMO, long enough that I’m glad this is a Sunday.

Earlier in this series:

  • On the felicities of graph-based game-board design: preliminaries
  • On the felicities of graph-based game-board design: two dazzlers
  • On the felicities of graph-based game-board design: three
  • On the felicities of graph-based game-board design: four
  • On the felicities of graph-based game-board design: five
  • On the felicities of graph-based game-board design: six
  • On the felicities of graph-based game-board design: seven
  • On the felicities of graph-based game-board design: eight
  • On play as wildness

    Saturday, September 24th, 2016

    [ by Charles Cameron — what’s true of hex maps is true of all mental models ]

    There’s a certain let-your-hair-down quality to play.

    It appears that one Tausendsassa Friedensreich Regentag Dunkelbunt Hundertwasser said or perhaps wrote, muttered, whispered, shouted, or simply thought out loud, “the straight line is a godless line” — at any rate, someone noticed and recorded the phrase, and now it’s scattered across the net and difficult to track to its source.


    But we do love order, don’t we?


    And so the rivers on our hexagonal maps all too easily follow the hexagons..


    when they’d more realistically cross over them, following their own courses:


    and note how easily even our efforts to bring natural variety to our hexagonal mappings conform more to hexagons than to variety.



    Zennist Thich Nhat Hanh in Listening Deeply for Peace writes:

    A traditional Vietnamese Zen garden is very different from a Japanese Zen garden. Our Zen gardens, called hon non bo, are wild and exuberant, more playful than the formal Japanese gardens with their restrained patterns. Vietnamese Zen gardens are seriously unserious. For us, the whole world is contained in this peaceful place. All activities of life unfold in true peace in the garden: in one part, children will be playing, and in another part, some elderly men will be having a chess game; couples are walking; families are having picnics; animals are free to wander around. Beautiful trees are growing next to abundant grasses and flowers. There is water, and there are rock formations. All ecologies are represented in this one microecology without discrimination. It is a miniature, peaceful world. It is a beautiful living metaphor for what a new global ethic could bring.


    Here is the wrestling of a tree with such angels as gravity, sun, wind and rain:


    Here is the wild calligraphy of the Rio Mamoré across the forests of the Amazon basin:


    From medieval gold leaf to Olympic gold

    Monday, August 15th, 2016

    [ by Charles Cameron — a voyage into nondualism via the coincidentia oppositorum ]

    Here from Dr Emily Steiner may be the widest rigorous gap-bridging DoubleQuotes I’ve ever seen:

    Kudos to Anthony Ervin for his gold!

    I’m not entirely sure there’s gold leaf in the image Dr Steiner uses to represent medieval manuscripts, though it certainly works for the genre as a whole, and I think I detect some gold leaf in the hearts of the flowers depicted..


    It would be foolish for me to claim to follow JL Usó-Doménech et al’s Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers, but the general notions of Cardinal Nicholas of Cusa (Cusanus), “That in God opposites coincide” and “That God is beyond the coincidence of opposites” rae pretty basic (with appropriate variations) to Carl Jung‘s psychology — and to my own thinking.

    Here, in Dr Steiner’s tweet, we have something that comes delightfully, playfully close to a coincidence of opposites. Indeed it is that possibility of evoking and annotating opposites in a manner than allows us to transcend them — as we could be said to transcend the two streams of vision in binocular vision, the two streams of hearing in stereophonic audition — that lies at the heart of my focus on DoubleQuoting.


    If the “new atheists” were a little more widely read, they might find themselves perplexed by the trans-logical implications of a God described thus by Cusanus:

    When we attempted to see Him beyond being and not-being, we were unable to understand how He could be visible. For He is beyond everything plural, beyond every limit and all unlimitedness; He is completely everywhere and not at all anywhere; He is of every form and of no form, alike; He is completely ineffable; in all things He is all things, in nothing He is nothing, and in Him all things and nothing are Himself; He is wholly and indivisibly present in any given thing (no matter how small) and, at the same time, is present in no thing at all.

    That’s a far harder concept — if it can even be called a concept — to deal with than the “seven day creator” God that is their usual mark. And yet there is no great logical space between Cusanus’ “He is completely ineffable” and the Athanasian Creed‘s ” The Father incomprehensible, the Son incomprehensible, and the Holy Spirit incomprehensible .. The Father eternal, the Son eternal, and the Holy Spirit eternal .. And yet they are not three eternals but one eternal .. As also there are not three uncreated nor three incomprehensible, but one uncreated and one incomprehensible.”

    Jasper Hoskins proposes [Jasper Hopkins, A concise introduction to the philosophy of Nicholas of Cusa] that in Cusanus’ view, “no finite mind can comprehend God, since finite minds cannot conceive of what it is like for God to be altogether undifferentiated.”


    There’s an exchange in Cusanus’ Trialogus de possest (“On actualized-possibility”) in Hoskins’ op. cit.., that sets forth instructions for reading propositions about God — which also make interesting reading in terms of the flexibility ofmmind andimagination necessary for reading poetry, myth, and scriptures:

    Bernard: I am uncertain whether in similar fashion we can fittingly say that God is sun or sky or man or any other such thing.

    Card. Nicholas of Cusa: We must not insist upon the words. For example, suppose we say that God is sun. If, as is correct, we construe this [statement] as [a statement] about a sun which is actually all it is able to be, then we see clearly that this sun is not at all like the sensible sun. For while the sensible sun is in the East, it is not in any other part of the sky where it is able to be. [Moreover, none of the following statements are true of the sensible sun:] “It is maximal and minimal, alike, so that it is not able to be either greater or lesser”; “It is everywhere and anywhere, so that it is not able to be elsewhere than it is”; “It is all things, so that it is not able to be anything other than it is”— and so on. With all the other created things the case is simnilar. Hence is does not matter what name you give to God, provided that in the foregoing manner you mentally remove the limits with respect to its possible being.

    We’re close here, to the zen notion of the finger pointing at the moon — except that here is is the moon pointing at what cannot even be located in either physical spacetime or conceptual space..


    and that’s the touch of gold in the heart of all flowers..

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